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hw1 - ORIE 3500/5500 Engineering Probability and Statistics...

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ORIE 3500/5500 – Engineering Probability and Statistics II Fall 2010 Assignment 1 Problem 1 We toss a coin 3 times. For this experiment we choose the sample space Ω = HHH, THH, HTH, HHT, TTH, THT, HTT, TTT , where T stands for tails and H stands for heads. a. Write down the outcomes comprising the following events: A : “we throw tails exactly twice”; B : “we throw tails at least twice”; C : “tails did not appear before a head appeared”; D : “the first throw results in tails” . b. Write down the outcomes comprising the following events: A c , A ( C D ), A D c . Problem 2 For events A and B , it is known that P ( A ) = . 6 , P ( B ) = . 7 but P ( A B ) is unknown. What are the smallest and the largest value that P ( A B ) may take? Problem 3 A town has 4 plumbers. If 4 houses have plumbing problems on a given day, what is the probability that exactly i plumbers are called, for i = 1 , 2 , 3 , 4. Explain what assumptions, if any, you are making.
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